Row-wise correlations in R

Question

I have two matrices of the same size. I would like to calculate the correlation coefficient between each pair of rows in these matrices; row 1 from A with row 1 B, row 2 from A

Answer 1

You could create vectorized functions that will calculate covariance and SD for you such as,

RowSD <- function(x) {
  sqrt(rowSums((x - rowMeans(x))^2)/(dim(x)[2] - 1))
}

VecCov <- function(x, y){
  rowSums((x - rowMeans(x))*(y - rowMeans(y)))/(dim(x)[2] - 1)
}

Then, simply do

VecCov(A, B)/(RowSD(A) * RowSD(B))

Answer 2

This should be fast:

cA <- A - rowMeans(A)
cB <- B - rowMeans(B)
sA <- sqrt(rowMeans(cA^2))
sB <- sqrt(rowMeans(cB^2))

rowMeans(cA * cB) / (sA * sB)